A Compliance Control of a Hyperredundant Robot

Abstract: The grasping control problem for a hyperredundant arm is studied. First, the dynamic model of the arm is analyzed. The control problems are divided in the subproblems: the position control in a desired reaching area, the control of the arm around the object-load and the force control of grasping. The difficulties determined by the complexity of the non-linear integral-differential equations are avoided by using a very basic energy relationship of this system. First, the dynamic control of the arm for a desired reaching area is inferred. Then, the position control and the force control for grasping are discussed. Numerical simulations are presented.

Mircea Ivănescu received his B.Sc. degree in Automatic Control in 1965 from the University Politehnica Bucharest. He received his Ph.D. degree in Control Systems in 1975. Now, he is a Professor at the Department of Mechatronics, University of Craiova. His research interests are focused on: Distributed Parameter Systems, Discrete Optimization Problems, Fuzzy Systems, Nonlinear Systems, and Robotics.

Mihaela Cecilia Florescu received her B. Sc. and M. Sc. degrees in Electromechanical Engineering in 1995 and 1996, respectively, from University of Craiova. Now she is a Lecturer at the Mechatronics Department, University of Craiova. Her research interests are focused on: Distributed Parameter Systems, Fuzzy Systems, and Robotics.

Nirvana Popescu received her B.Sc. and M. Sc. degrees in Computer Science in 1997 and 1998, respectively, from University Politehnica, Bucharest. She received the Ph.D. degree in Computer Science in 2003 from University Politehnica, Bucharest. Now she is a Lecturer at the Computer Department, University Politehnica, Bucharest. Her research interests are focused on: Fuzzy Systems, Digital Circuits, Intelligent Adaptive Systems, and Vision Control.

Decebal Popescu received his B. Sc. and M. Sc. degrees in Computer Science in 1997 and 1998, respectively, from University Politehnica, Bucharest. He received the Ph.D. degree in Computer Science in 2003 from University Politehnica, Bucharest. Now he is a Lecturer at the Computer Department, University Politehnica, Bucharest. His research interest is focused on: Fuzzy Systems, Digital Circuits, VLSI circuits, and Robotics.

The control of a hyperredundant manipulator is very complex and a great number of researchers have tried to offer solutions for this difficult problem. In [7] it was analyzed the control by cables or tendons meant to transmit forces to the elements of the arm in order to closely approximate the arm as a truly continuous backbone. In [6], Gravagne analyzed the kinematical model of “hyper-redundant” robots, known as “continuum” robots. Important results were obtained by Chirikjian and Burdick [3, 4], which laid the foundations for the kinematical theory of hyper-redundant robots. Mochiyama has also investigated the problem of controlling the shape of an HDOF rigid-link robot with two-degree-of-freedom joints using spatial curves [11]. In [11, 14] it is presented the “state of art” of continuum robots, outline their areas of application and introduce some control issues.

The difficulty of the dynamic control is determined by integral-partial-differential models with high nonlinearities that characterize the dynamic of these systems. In [8] the dynamic model for 3D space is inferred and a control law based on the energy of the system is analyzed.

In this paper, the problem of a class of hyperredundant arms with continuum elements that performs the grasping function by coiling is discussed. The difficulties determined by the complexity of the non-linear integral-differential equations, that represent the dynamic model of the system, are avoided by using a very basic energy relationship of this system. Energy-based control laws are introduced for the position control problem. A force control method is also proposed.

The paper is organized as follows: section 2 presents the basic principles of a hyperredundant structure with continuum elements; section 3 studies the dynamic model; section 4 discusses the both problem of grasping by coiling, the position control and force control; section 5 verifies by computer simulation the control laws.

6. Conclusion

The paper treats the control problem of a hyperredundant robot with continuum elements that performs the coil function for grasping. The structure of the arm is given by flexible composite materials in conjunction with active-controllable electro-rheological fluids. The dynamic model of the system is inferred by using Lagrange equations developed for infinite dimensional systems.

The grasping problem is divided in two subproblems: the position control and force control. The difficulties determined by the complexity of the non-linear integral-differential equations are avoided by using a very basic energy relationship of this system and energy-based control laws are introduced for the position control problem. Numerical simulations are presented.

Ivanescu, M., Position Dynamic Control for a Tentacle Manipulator, Proc. IEEE International Conference on Robotics and Automation, Washington, A1-15, May 2002, pp. 1531-1539.

Ivanescu,M., M.C. Florescu, N. Popescu, D. Popescu, position and Force Control of the Grasping Function for a Hyperredundant Arm, Proc. of IEEE International Conference on Robotics and Automation, Pasadena, California, 2008 (to be published).

Mochiyama, H., H. Kobayashi, The Shape Jacobian of a Manipulator with Hyper Degrees of Freedom, Proc. 1999 IEEE International Conference on Robotics and Automation, Detroit, May 1999, pp. 2837- 2842.